Matter couplings and equivalence principles for soft scalars
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Springer
Received: February 25, 2020 Accepted: June 10, 2020 Published: July 8, 2020
Matter couplings and equivalence principles for soft scalars
a
CERCA, Department of Physics, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44106, U.S.A. b Center for Theoretical Physics, Department of Physics, Columbia University, New York, NY 10027, U.S.A.
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] Abstract: Scalar effective field theories with enhanced soft limits behave in many ways like gauge theories and gravity. In particular, symmetries fix the structure of interactions and the tree-level S-matrix in both types of theories. We explore how this analogy persists in the presence of matter by considering theories with additional fields coupled to the Dirac-Born-Infeld (DBI) scalar or the special galileon in a way that is consistent with their symmetries. Using purely on-shell arguments, we show that these theories obey analogues of the S-matrix equivalence principle whereby all matter fields must couple to the DBI scalar or the special galileon through a particular quartic vertex with a universal coupling. These equivalence principles imply the universality of the leading double soft theorems in these theories, which are scalar analogues of Weinberg’s gravitational soft theorem, and can be used to rule out interactions with massless higher-spin fields when combined with analogues of the generalized Weinberg-Witten theorem. We verify in several examples that amplitudes with external matter fields nontrivially exhibit enhanced single soft limits and we show that such amplitudes can be constructed using soft recursion relations when they have sufficiently many external DBI or special galileon legs, including amplitudes with massive higher-spin fields. As part of our analysis we construct a recently conjectured special galileon-vector effective field theory. Keywords: Effective Field Theories, Global Symmetries, Scattering Amplitudes, Spontaneous Symmetry Breaking ArXiv ePrint: 1911.04490
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)056
JHEP07(2020)056
James Bonifacio,a Kurt Hinterbichler,a Laura A. Johnson,a Austin Joyceb and Rachel A. Rosenb
Contents 1 Introduction
1
2 Coupling to matter 2.1 DBI theory 2.2 Special galileon
4 4 6 8 9 10 11 13
4 Soft scalar equivalence principles 4.1 DBI equivalence principle 4.2 Special galileon equivalence principle 4.3 No massless higher-spin interactions 4.4 Double soft theorems
15 15 18 19 20
5 Soft recursion 5.1 Review of soft recursion relations 5.2 All-line soft shift for massless matter amplitudes 5.3 All-but-r-line soft shift
22 23 24 25
6 “Gravitational” phenomenology 6.1 Effective gravitational force 6.2 Cosmology
26 26 29
7 Conclusions
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A Degree of freedom counting
31
B Ruling out other quartic vertices
32
1
Introduction
Aspects of gravitational physics remain mysterious even today, a century after the discov
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